3. Interval estimation of: population proportion it. has EL Think about the following game: A fair coin is tossed 10 times. Each time the toss results In heads, you receive $1D: for tails. you get nothing. 1u'ilhat is the maximum amount you would pay to play the game? Dene a success as a toss that lands on heads. Then the probability of a success is LIE. and the expected number or suocesses after to tosses is 1U{D.5} = 5. Since each suocess pays $10, the total amount you would expect to win Is 5E$1D} = tso. Suppose each person in a random sample of 1,536 adults between the ages of 11 and 55 is invited to play this game. Each person is asked the maximum amount they are willing to pay to play. (Data source: These data were adapted from Ben Hansour, Selima, Jouini, Elyes, Marin, Jean-MicheL Happ. Clotilde, 61 Robert. Chrisb'an. {ZOE-E]. are risk-averse agents more optimistic? A. Bayesian estimation approach. Journal of Applied Econometrics, 23(5), BdBBE.) Someone is described as \"risk neutral\"Er if the maximum amount he or she is willing to pair to plEI'ir is equal to $50. the game's expected value. Suppose in this LEE-person sample, 34 people are risk neutral. Let p denote the proportion ofthe adult populab'on aged 22 to 55 who are risk neutral and 1 p. the proportion ofthe same population who are not risk neutral. Use the sample results to estimate the proportion p. The proportion p of adults in the sample who are risk neutral is . The proportion 1 - p or adults In the sample who are not nsk neutral is You can con-dude that the sampling distribution of p can be approximated by a normal distribution, because . The sampling distribution of p has an esprit-rated standard deviation of Standard No map! 1" Random Deviation I I Use the Distributions tool to develop a 99% condence interval estimate of the prooortlon of adults aged 12 to 55 who are net nautnal. You can be 99% condent that the Mental estlmate to lncludes the populatlon proportldn p. the proportlon of adults aged 22 to 55 who are rlslt neutral